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# Chapter 4

### Matrices

Question | Answer |
---|---|

What is a matrix? | A matrix is a rectangular arrangement of objects, each of which is called an element of the matrix. One use of matrices is to store data. |

How are two matrices equal? | Two matrices are equal matrices if and only if they have the same dimensions and their corresponding elements are equal. |

What is the definition of matrix addition? | If two matrices A and B have the same dimensions, their sum A + B is the matrix in which each element is the sum of the corresponding elements in A and B. |

What is scalar multiplication? | The product of a scalar k and a matrix A is the matrix kA in which each element is k times the corresponding element in A. |

What is the definition of Matrix Multiplication? | Suppose A is an m x n matrix and B is an n x p matrix. Then the product A X B(or AB)is the m x p matrix whose element in row i and column j is the product of row i of A and column j of B. |

What is the definition of a matrices for size changes? | For any k not equal to zero, the transformation that maps (s,y) onto (kx,ky) is called the size change with center (0,0) and magnitude k, and is denoted S sub k. S sub k (x,y)= (kx,ky) |

What is the definition of matrices for scale changes? | For any nonzero numbers a and b, the transformation that maps (x,y) onto (ax,by) is called the scale change with horizontal magnitude a and vertical magnitude b, and is denoted S sub a,b. |

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Southlawn